papaya
Class MDS

java.lang.Object
  papaya.MDS

public final class MDS
extends Object

Contains methods for performing but classical and non-classical multidimensional scaling.

For an m-by-n input matrix with m observations and n variables, the output D is the symmetric m-by-m matrix with zeros along the diagonals and element ij specifying the distance between rows i and j.

Method Summary

static float[][]

classical(float[][] D, int p, boolean showEigenvalues) Performs classical (metric) multidimensional scaling, on an input matrix of Distances (computed using e.g.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

classical

public static float[][] classical(float[][] D,
                                  int p,
                                  boolean showEigenvalues)

Performs classical (metric) multidimensional scaling, on an input matrix of Distances (computed using e.g. Distance ) and outputs the best-fitting p-dimensional configuration of points (p<N). The output matrix Y has p columns with rows giving the coordinates of the points chosen to represent the dissimilarities. When D corresponds to the Euclidian distance matrix, the p dimensional coordinates correspond exactly to the first p principal components.

Remarks

• If p > kwhere k is the number of positive eigenvalues of Y*Y', then only the first k columns of Y are computed.
• Set showEigenvalues to true to print the values of the "scalar product matrix" Y*Y' to the screen. (This is a good idea if you want to know how well the first p dimensions captures most of the variation in D.

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Parameters:

D - the input distance matrix (see Distance)

p - the dimension (number of columns) of the output matrix.

showEigenvalues - whether to print the eigenvalues to the screen or otherwise.

Returns:

Y, N-by-p (or N-by-k) matrix consisting of N points in each of the p (or k) dimensions.